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Discrete optimization

About: Discrete optimization is a research topic. Over the lifetime, 4598 publications have been published within this topic receiving 158297 citations. The topic is also known as: discrete optimisation.


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Journal ArticleDOI
TL;DR: This problem is extensively considered in the literature and includes the familiar optimal regulator and optimal tracking problems for linear systems with a quadratic performance criterion and the solution may be obtained by the following rather direct method.
Abstract: This problem is extensively considered in the literature and includes the familiar optimal regulator and optimal tracking problems for linear systems with a quadratic performance criterion (see [1]). The solution may be obtained by the following rather direct method (see [2], Section 4.4). Observe that H1 × H3, equipped with the usual inner product, is a Hilbert space whose norm is computed by [(u, x)] 2 = I] u []2 + I I x 112 for (u, x) ~ Hx × H3. Note also that the infimum of J over H1 is the distance of (0, N~:) ~ H1 x H3 from the graph of T. Since the graph of T is a closed linear subspace, this infimum is attained uniquely by the orthogonal projection of(0, N~:) on this subspace. It is then easily established that the optimal control is given by

28 citations

Journal ArticleDOI
TL;DR: In this paper, a bi-level optimization problem covering upper (design) and lower (operation) levels is defined and a solution procedure for bilevel optimization problems is presented, where the values of the control and state variables change over a predefined time horizon and several competing criteria are optimized simultaneously.
Abstract: In this article, a bi-level optimization problem covering upper (design) and lower (operation) levels is defined and a solution procedure for bi-level optimization problems is presented. This is devised as a dynamic multiobjective optimization problem, i.e. the values of the control and state variables change over a predefined time horizon and several competing criteria are optimized simultaneously. Moreover, the interaction between the upper and lower levels is analysed. The benefits of bi-level dynamic multiobjective optimization are illustrated in detail by examining an industrial case in which the design of a paper mill (upper level) and the mill operation (lower level) are optimized at the same time. However, the problem definition and the solution procedure are not limited to any specific application but can be exploited in many different industrial areas.

28 citations

Proceedings ArticleDOI
Martin Strrelec1, Jan Berka1
01 Oct 2013
TL;DR: Energy management system based on ADP is introduced and its behavior is demonstrated on small scale Microgrid which is connected to distribution network and includes wind turbine, chiller plant, thermal storage and cooling load.
Abstract: Microgrid energy management stands for challenging optimization problem where continuous (economic dispatch) and discrete optimization (unit commitment) tasks are solved Often Microgrid optimization leads to complex problem where optimization methods usually meet curse of dimensionality We adopt approximate dynamic programming (ADP) as the promising optimization technique which can overcome curse of dimensionality In this paper, energy management system based on ADP is introduced and its behavior is demonstrated on small scale Microgrid which is connected to distribution network and includes wind turbine, chiller plant, thermal storage and cooling load The paper describes policy search approach to ADP and selected approximation architectures in the context of energy optimization The ADP results are compared with the results of the solution based on dynamic programming approach

28 citations

Book
31 Jul 2000
TL;DR: The following topics are important teaching operation research: games theory, decision theory, utility theory, queuing theory, scheduling theory, discrete opti­ mization, and the connection with global optimization is shown considering seven mathematical models.
Abstract: The following topics are important teaching operation research: games theory, decision theory, utility theory, queuing theory, scheduling theory, discrete opti­ mization. These topics are illustrated and the connection with global optimization is shown considering the following mathematical models: - competition model with fixed resource prices, Nash equilibrium, - competition model with free resource prices, Walras equilibrium, - inspector's problem, multi-stage game model, - "Star War" problem, differential game model, - "Portfolio" problem, resource investment model, - exchange rate prediction, Auto-Regression-Moving-Average (ARMA) model, - optimal scheduling, Bayesian heuristic model, - "Bride's" problem, sequential statistical decisions model. The first seven models are solved using a set of algorithms of continuous global and stochastic optimization. The global optimization software GM (see (19)) is used. The underlying theory of this software and algorithms of solution are described in (19, 17). The last model is an example of stochastic dynamic programming. For better understanding, all the models are formulated in simplest terms as "class­ room" examples. However, each of these models can be regarded as simple representations of important families of real-life problems. Therefore the models and solution algorithms may be of interest for application experts, too. The paper is split into two parts. In the part one (18) the first five models are de­ scribed. In this part the rest three models and accompanyiing software are considered.

28 citations

Journal ArticleDOI
TL;DR: In this article, an effective numerical procedure for reliability-based design optimization (RBDO) of nonlinear inelastic steel frames by integrating a harmony search technique (HS) for optimization and a robust method for failure probability analysis is proposed.
Abstract: This paper proposes an effective numerical procedure for reliability-based design optimization (RBDO) of nonlinear inelastic steel frames by integrating a harmony search technique (HS) for optimization and a robust method for failure probability analysis. The practical advanced analysis using the beam-column approach is used for capturing the nonlinear inelastic behaviors of frames, while a detail implement of HS for discrete optimization of steel frames is introduced. The failure probability of structures is evaluated by using the combination of the improved Latin Hypercube (IHS) and a new effective importance sampling (EIS). The efficiency and accuracy of the proposed procedure are demonstrated through three mathematical examples and five steel frames. The results obtained in this paper prove that the proposed procedure is computationally efficient and can be applied in practical design. Furthermore, it is shown that the use of nonlinear inelastic analysis in the optimization of steel frames yields more realistic results.

28 citations


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Performance
Metrics
No. of papers in the topic in previous years
YearPapers
202313
202236
2021104
2020128
2019113
2018140